Shakhtar showed promise on the counter but were unable to stop Dortmund confirming their status as a side to avoid in this season's competition.
Here, Sports Mole looks back at a statement of intent from the reigning Bundesliga champions.
On target 11
On target 7
Was the result fair?
Dortmund fully merited their emphatic victory thanks to an all-action display which featured energy and desire all over the pitch. Shakhtar threatened fleetingly on the break but were outclassed for long spells and ultimately paid the price for conceding twice at home in the first leg.
Slick interplay and pressing high on the pitch have been Dortmund trademarks under Jurgen Klopp, and tonight was no different. A fluid trio of Robert Lewandowski, Marco Reus and Mario Gotze wreaked havoc all night with slick passing and movement that Shakhtar could not match. Ilkay Gundogan is an unsung hero for the German giants and didn't put a foot wrong all night in a deeper holding position.
The visitors showed promise on the counter but were undermined by slack defending throughout. An unstable back four lacked concentration throughout and never found an effective tactic to deal with the Lewandowski's clever runs from deep.
Sports Mole's man of the match
Mario Gotze: The talented playmaker was a constant thorn in Shakhtar's side with an intelligent presence in the final third. Gotze deserved his slick of luck for Dortmund's second goal and came off the flank to deadly effect consistently.
Andriy Pyatov killed the tie stone dead when he spilled Gundogan's shot early in the second half. Blaszczykowski was on hand to expose the goalkeeper's poor attempt to clear and dink over his flailing dive for Dortmund's third and final goal.
Dortmund: Klopp's men return to the fight for second place in the Bundesliga with a home match against Fortuna Dusseldorf this weekend.
Shakhtar: The Ukrainian champions must concentrate on their title defence with their second league match of 2013 away to Vorskla on Sunday.